Problem # 28
We are told 1st and last terms of a 14 elemnt GP add to 7 AND the 5th term is the geometric mean of the 2nd and 14th term. Shown to the right.
The equations
... and 4 complex roots! --->
using just the positive 1
THE ANSWER
so the sequence is A = {7/2,7/2,....7/2}
Problem # 25
AP
(working forwards)
GP (working backwards)
(2 eq with variables)
solving for d in left eq and substituting into right eq:
solving for r
Note:
r =-6 is associated with d = -1.75 AND r = 3/2 is associated with d = 2.
solving for d
A = { 2, 4, 6, 9 }
OR
A = { 2, 1/4, -3/2, 9 }